An iterative working-set method for large-scale nonconvex quadratic programming We consider a working-set method for solving large-scale quadratic programming problems for which there is no requirement that the objective function be convex. The methods are iterative at two levels, one level relating to the selection of the current working set, and the second due to the method used to solve the equality-constrained problem for this working set. par A preconditioned conjugate gradient method is used for this inner iteration, with the preconditioner chosen especially to ensure feasibility of the iterates. The preconditioner is updated at the conclusion of each outer iteration to ensure that this feasibility requirement persists. The well-known equivalence between the conjugate-gradient and Lanczos methods is exploited when finding directions of negative curvature. par Details of an implementation -- the Fortran 90 package QPA in the forthcoming GALAHAD library -- are given.

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  2. Curtis, Frank E.; Han, Zheng; Robinson, Daniel P.: A globally convergent primal-dual active-set framework for large-scale convex quadratic optimization (2015)
  3. Gill, Philip E.; Wong, Elizabeth: Methods for convex and general quadratic programming (2015)
  4. Gill, Philip E.; Wong, Elizabeth: Sequential quadratic programming methods (2012)
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  6. Gould, Nicholas I.M.; Robinson, Daniel P.: A second derivative SQP method: local convergence and practical issues (2010)
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  14. Gould, Nicholas I.M.; Toint, Philippe L.: An iterative working-set method for large-scale nonconvex quadratic programming (2002)
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